You changed the audio output mode of FMOD Studio only. Not unity.
When you selected ASIO it takes over the windows audio system, ie with exclusive audio control.
When you then ran unity (with WASAPI output as shown in the error messages) it failed because ASIO is holding control of the windows audio.
The best idea would be to alter the FMOD startup sequence in unity, and not adjust the FMOD Studio audio output mode.
During development you cannot have a WASAPI and ASIO application (or 2 ASIO applications) running simultaneously